15 18 24 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 18   c = 24

Area: T = 134.8311144399
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 38.62548328731° = 38°37'29″ = 0.67441305067 rad
Angle ∠ B = β = 48.50991831443° = 48°30'33″ = 0.84766449633 rad
Angle ∠ C = γ = 92.86659839826° = 92°51'58″ = 1.62108171836 rad

Height: ha = 17.97774859199
Height: hb = 14.98112382666
Height: hc = 11.23659286999

Median: ma = 19.8433134833
Median: mb = 17.87545629317
Median: mc = 11.42436596588

Inradius: r = 4.73109173473
Circumradius: R = 12.01550281837

Vertex coordinates: A[24; 0] B[0; 0] C[9.93875; 11.23659286999]
Centroid: CG[11.31325; 3.74553095666]
Coordinates of the circumscribed circle: U[12; -0.60107514092]
Coordinates of the inscribed circle: I[10.5; 4.73109173473]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.3755167127° = 141°22'31″ = 0.67441305067 rad
∠ B' = β' = 131.4910816856° = 131°29'27″ = 0.84766449633 rad
∠ C' = γ' = 87.13440160174° = 87°8'2″ = 1.62108171836 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 15 ; ; b = 18 ; ; c = 24 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 15+18+24 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-15)(28.5-18)(28.5-24) } ; ; T = sqrt{ 18179.44 } = 134.83 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 134.83 }{ 15 } = 17.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 134.83 }{ 18 } = 14.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 134.83 }{ 24 } = 11.24 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 15**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 38° 37'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-15**2-24**2 }{ 2 * 15 * 24 } ) = 48° 30'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-15**2-18**2 }{ 2 * 18 * 15 } ) = 92° 51'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 134.83 }{ 28.5 } = 4.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 38° 37'29" } = 12.02 ; ;




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